Kaggle Competition https://www.kaggle.com/c/web-traffic-time-series-forecasting

Using Kaggel competition as:

Data

Data sets are available here for download:
https://www.kaggle.com/c/web-traffic-time-series-forecasting/data

Data Structure (and Size)

Information based on full dataset for reference.

train:

  • 145K rows x 551 vars
  • each row has info for one article based on:
    • article title from URL
    • locale of wikipedia (en.wikipedia.org, zh.wikipedia.org, etc)
    • access type (all-access, desktop, etc)
    • agent (all-agents, spider, etc)
  • cols are dates in format X2015.08.02

key:

  • 8.7M rows x 2 vars
  • this file has article info with date appended and a corresponding id number
  • i believe only used for uploading data to Kaggle

Sampling

Due to the size of data, need to take a sample and work with that.

Sample can be based on:

  • random selection of rows (not so useful in this case)
  • selected pages
    • topic?
    • key words?
  • incorporate dimensions:
    • locale (en.wikipedia)
    • type of access (device?): eg. ‘desktop’
    • ‘agent’ (source?): eg. ‘spider’

First crack:

  • filter full train_1.csv for “en.wikipedia” and save
Error in eval(expr, envir, enclos) : object 'train1' not found
  • reduces down to 24k rows
  • still 50MB

Second crack:

  • select pages (including variations by user agent, etc):
    • Main page (‘Main_Page_en’)
    • Howard Hughes (‘Howard_Hughes_en’)
    • Orange is the New Black (‘Orange_is_the_New_Black_en’)
  • 15 rows
  • 54KB - much better for small computer

  • SAVE AND USE

subject <- read.csv("data-input/subject.csv", stringsAsFactors=FALSE)

WRANGLE SUBJECT DATA

Structure (extend for more date columns):

subject.temp <- subject[,c(1:3)]
str(subject.temp)
'data.frame':   12 obs. of  3 variables:
 $ Page       : chr  "Howard_Hughes_en.wikipedia.org_desktop_all-agents" "Main_Page_en.wikipedia.org_desktop_all-agents" "Orange_Is_the_New_Black_en.wikipedia.org_desktop_all-agents" "Howard_Hughes_en.wikipedia.org_all-access_spider" ...
 $ X2015.07.01: int  75357 11952559 28486 137 17207 168 109821 20381245 65947 34167 ...
 $ X2015.07.02: int  5396 12344021 26685 113 14756 132 13122 20752194 60189 7528 ...

Pages:

subject <- subject %>% arrange(Page)
package 㤼㸱bindrcpp㤼㸲 was built under R version 3.3.3
subject$Page
 [1] "Howard_Hughes_en.wikipedia.org_all-access_all-agents"          
 [2] "Howard_Hughes_en.wikipedia.org_all-access_spider"              
 [3] "Howard_Hughes_en.wikipedia.org_desktop_all-agents"             
 [4] "Howard_Hughes_en.wikipedia.org_mobile-web_all-agents"          
 [5] "Main_Page_en.wikipedia.org_all-access_all-agents"              
 [6] "Main_Page_en.wikipedia.org_all-access_spider"                  
 [7] "Main_Page_en.wikipedia.org_desktop_all-agents"                 
 [8] "Main_Page_en.wikipedia.org_mobile-web_all-agents"              
 [9] "Orange_Is_the_New_Black_en.wikipedia.org_all-access_all-agents"
[10] "Orange_Is_the_New_Black_en.wikipedia.org_all-access_spider"    
[11] "Orange_Is_the_New_Black_en.wikipedia.org_desktop_all-agents"   
[12] "Orange_Is_the_New_Black_en.wikipedia.org_mobile-web_all-agents"

3 components to Page:

  1. Subject
  2. Access: ‘all-access’, ‘desktop’, ‘mobile’
  3. Agent: ‘all-agents’, ‘spider’

Note that ‘all-access-all-agents’ is the total of the other variations.

Time Series Data Example

Try with one page variation.

main.all.all <- subject %>% filter(Page=="Main_Page_en.wikipedia.org_all-access_all-agents")
main.all.all.ts <- main.all.all %>% gather(key=date, value=views, -Page)
main.all.all.ts$date <- sub("X", "", main.all.all.ts$date) 
main.all.all.ts$date <- as.Date(main.all.all.ts$date, format="%Y.%m.%d")
main.all.all.ts$index <- 1:nrow(main.all.all.ts) ## index for time series data points
summary(main.all.all.ts)
     Page                date                views              index      
 Length:550         Min.   :2015-07-01   Min.   :13658940   Min.   :  1.0  
 Class :character   1st Qu.:2015-11-15   1st Qu.:18098508   1st Qu.:138.2  
 Mode  :character   Median :2016-03-31   Median :19457533   Median :275.5  
                    Mean   :2016-03-31   Mean   :21938511   Mean   :275.5  
                    3rd Qu.:2016-08-15   3rd Qu.:22212934   3rd Qu.:412.8  
                    Max.   :2016-12-31   Max.   :67264258   Max.   :550.0  
chart.title <- "Daily Views for Main page - all access, all agents"
plot.ts1 <- ggplot(main.all.all.ts, aes(x=date, y=views))+geom_line()+
  scale_y_continuous(labels=comma, expand=c(0,0))+theme_classic()+ggtitle(chart.title)
ggplotly(plot.ts1)
We recommend that you use the dev version of ggplot2 with `ggplotly()`
Install it with: `devtools::install_github('hadley/ggplot2')`

Time Series Modeling (single time series example)

Take the example of Main page, all access, all agent to build time series model based on single time series.

Approach 1: Linear Smoothing (Loess)

References:

Info:

  • Loess is short for ‘local regression’ - it is the most common method for smoothing volatile time series
  • Uses least squares regression on subsets of data (can control how finely grained the subsets are)
  • ggplot2 uses loess as default for geom_smooth when less than 1,000 data points
  • Loess using lots of memory and so is not suitable for huge data sets

Analyze (visualize) smoothing models

SAME CHART AS ABOVE WITH LOESS SMOOTHING ADDED (ggplot2 defaults)

plot.ts1+geom_smooth(method='loess')

  • Increase granularity with span (between 0-1, higher is smoother)
chart.title <- "Same Plot with loess span set lower for more granularity"
plot.ts1+geom_smooth(method='loess', span=0.3)

  • can layer in multiple loess smoothed lines for comparison (confidence intervals removed)
plot.ts1+
  geom_smooth(formula=y ~ x, method='loess', span=0.2, color='red', se=FALSE)+
  geom_smooth(method='loess', span=0.4, color='orange', se=FALSE)+
  geom_smooth(method='loess', span=0.6, color='green', se=FALSE)+
  geom_smooth(method='loess', span=0.8, color='purple', se=FALSE)+
  ggtitle("Same Plot with various smoothing lines (span adjusted, no conf. int.)")

Making a Prediction based on loess model

Get loess model from existing data

loess1 <- loess(views ~ as.numeric(date), data=main.all.all.ts, span=0.3)
summary(loess1)
Call:
loess(formula = views ~ as.numeric(date), data = main.all.all.ts, 
    span = 0.3)

Number of Observations: 550 
Equivalent Number of Parameters: 10.02 
Residual Standard Error: 5885000 
Trace of smoother matrix: 11.07  (exact)

Control settings:
  span     :  0.3 
  degree   :  2 
  family   :  gaussian
  surface  :  interpolate     cell = 0.2
  normalize:  TRUE
 parametric:  FALSE
drop.square:  FALSE 

Apply Loess model to future time periods

## extend date range for prediction period
ndays <- 30 ## number of days to predict
pred.period <- data.frame(date=seq(min(main.all.all.ts$date),max(main.all.all.ts$date+ndays), by='days'))
## prediction with loess1 doesn't work because default loess doesn't extrapolate 
#predict(loess1, pred.period, se=TRUE)
## new loess model: add control=...
sp <- 0.45 ## set span for model: lower number puts more weight on recent
loess2 <- loess(views ~ as.numeric(date), data=main.all.all.ts, control=loess.control(surface = 'direct'), span=sp)
## plot actual data with fitted data from model
plot.ts1+geom_line(aes(date, loess2$fitted, color='model'))

## predict with new loess model - extended period
pr <- predict(loess2, as.numeric(pred.period$date), se=TRUE)
## prediction (including existing data)
#pr[[1]] ## first object is prediction
## new data frame with dates and prediction
prediction <- pred.period %>% mutate(views.pred=pr[[1]])
## join date rate for prediction with existing data
main.pred <- left_join(prediction, main.all.all.ts, by='date') %>% select(-index)
## plot the result
chart.title <- "Daily Views for Main Page with Loess Model"
plot.ts2 <- ggplot(main.pred, aes(x=date, y=views))+geom_line()+
  scale_y_continuous(labels=comma, expand=c(0,0))+theme_classic()+
  ggtitle(chart.title)+geom_line(aes(date, views.pred, color='model+prediction'))
ggplotly(plot.ts2)
We recommend that you use the dev version of ggplot2 with `ggplotly()`
Install it with: `devtools::install_github('hadley/ggplot2')`

Span: 0.45 Number of days predicted: 30

Conclusion

  • Loess is great for smoothing a line to highlight general pattern
  • maybe not great for time series prediction - subject to manipulation

Approach 2

Reference: * http://r-statistics.co/Time-Series-Analysis-With-R.html

Convert data from data frame to time series object

  • Set up time series so that can apply time series functions for decomposition, etc
## time series forumlation examples from above reference
# ts (inputData, frequency = 4, start = c(1959, 2)) # frequency 4 => Quarterly Data
# ts (1:10, frequency = 12, start = 1990) # freq 12 => Monthly data. 
# ts (inputData, start=c(2009), end=c(2014), frequency=1) # Yearly Data
## See Notes below for explanation of frequency
ts.Main <- ts(main.all.all.ts$views, frequency=365, start=c(year(min(main.all.all.ts$date)), month(min(main.all.all.ts$date)), day(min(main.all.all.ts$date))))
ts.Main.all.all.wk <- ts(main.all.all.ts$views, frequency=52, start=c(year(min(main.all.all.ts$date)), month(min(main.all.all.ts$date)), day(min(main.all.all.ts$date))))

Notes:

  • since it is daily data, time series frequency=365 (days in yr)
  • however, because there is total 550 data points, not enough data for seasonality component to be estimated (need at least two iterations)
    • will get error: “time series has no or less than 2 periods”"
  • so…used frequency=52 to treat the time series as weekly data for illustration purposes
  • (great for illustrative purposes but might be hard to get a reliable prediction)

More on ‘time series has no or less than 2 periods’ error:
* https://stat.ethz.ch/pipermail/r-help/2013-October/361047.html

Decomposition

Using ‘decompose’

decomposedRes <- decompose(ts.Main.all.all.wk, type='additive') ## type='mult' if multiplicative; 'additive' if additive
plot(decomposedRes)

Using ‘stl’


stl.style <- stl(ts.Main.all.all.wk, s.window='periodic')
plot(stl.style)

Prediction

https://a-little-book-of-r-for-time-series.readthedocs.io/en/latest/

Reverting back to original data and forging ahead with prediction.

ts.Mainforecast
Holt-Winters exponential smoothing without trend and without seasonal component.

Call:
HoltWinters(x = ts.Main, beta = FALSE, gamma = FALSE)

Smoothing parameters:
 alpha: 0.9999487
 beta : FALSE
 gamma: FALSE

Coefficients:
      [,1]
a 26149449
  • alpha close to 1 means heavy weighting on recent (needs confirmation)

  • plotting forecast against actual

Forecast

---
title: 'Time Series Forecasting (based on Kaggle Competition: Web Traffic Forecasting)'
output:
  html_document: default
  html_notebook: default
---

Kaggle Competition
https://www.kaggle.com/c/web-traffic-time-series-forecasting 

Using Kaggel competition as:

* source of data in related field
* learn from approaches by others (kernels, etc)

```{r include=FALSE}
knitr::opts_chunk$set(echo = TRUE,
                      message=FALSE,
                      warning=FALSE)
## load typical libraries

library(tidyverse)
#library(dplyr)
#library(tidyr)
#library(ggplot2)
library(plotly)
library(scales)
library(lubridate)
library(forecast)

```
## Data

Data sets are available here for download: <br>
https://www.kaggle.com/c/web-traffic-time-series-forecasting/data

* initial data downloaded from Kaggle and saved in 'data-input' folder:
    + train_1.csv (265MB)
    + key_1.csv (711MB)
    
* due to size of dataset, not uploaded to git repository
* work with sample instead of full data set


```{r IMPORT AND INSPECT FULL DATA SET, echo=FALSE}
## if necessary, data can be downloaded and imported
## prefer to use small sample as explained further down the file
## warning: this can take a long time due to file size (10 min or so on MS Surface)
# train1 <- read.csv("data-input/train_1.csv", stringsAsFactors = FALSE)
# key1 <- read.csv("data-input/key_1.csv", stringsAsFactors = FALSE)
# 
# head(key1)
# head(train1)
```

### Data Structure (and Size)

Information based on full dataset for reference.

**train:**

* 145K rows x 551 vars
* each row has info for one article based on:
    + article title from URL
    + locale of wikipedia (en.wikipedia.org, zh.wikipedia.org, etc)
    + access type (all-access, desktop, etc)
    + agent (all-agents, spider, etc)
* cols are dates in format X2015.08.02

**key:**

* 8.7M rows x 2 vars
* this file has article info with date appended and a corresponding id number
* i believe only used for uploading data to Kaggle

#### Sampling

Due to the size of data, need to take a sample and work with that.

Sample can be based on:

* random selection of rows (not so useful in this case)
* selected pages 
    + topic?
    + key words?
* incorporate dimensions:
    + locale (en.wikipedia)
    + type of access (device?): eg. 'desktop'
    + 'agent' (source?): eg. 'spider'
    
First crack:

* filter full train_1.csv for "en.wikipedia" and save

```{r, echo=FALSE}
## start with filter for en

# train1.en <- train1 %>% filter(grepl("en.wikipedia", train1$Page, ignore.case=TRUE))
# # looks good - save for future use
# write.csv(train1.en, "data-input/train-en.csv", row.names=FALSE)
# 
# train.en <- read.csv("data-input/train-en.csv", stringsAsFactors = FALSE)
```
* reduces down to 24k rows
* still 50MB

Second crack:

* select pages (including variations by user agent, etc):
    + Main page ('Main_Page_en')
    + Howard Hughes ('Howard_Hughes_en')
    + Orange is the New Black ('Orange_is_the_New_Black_en')
    
```{r SUBJECT FILTER AND SAVE, echo=FALSE}
# train.subject <- train.en %>%
#   filter(grepl("^Main_Page_en|Howard_Hughes_en|Orange_Is_the_New_Black_en", train.en$Page, ignore.case=FALSE))
# 
# write.csv(train.subject, "data-input/subject.csv", row.names = FALSE)
```

* 15 rows
* 54KB - much better for small computer

* SAVE AND USE

```{r SUBJECT IMPORT}
subject <- read.csv("data-input/subject.csv", stringsAsFactors=FALSE)
```

### WRANGLE SUBJECT DATA

Structure (extend for more date columns):

```{r WRANGLE SUBJECT}
subject.temp <- subject[,c(1:3)]
str(subject.temp)
```

Pages: 

```{r}
subject <- subject %>% arrange(Page)
subject$Page

```

3 components to Page:

1. Subject
2. Access: 'all-access', 'desktop', 'mobile'
3. Agent: 'all-agents', 'spider'

Note that 'all-access-all-agents' is the total of the other variations.

### Time Series Data Example

Try with one page variation.

```{r MAIN ALL CLEAN}
main.all.all <- subject %>% filter(Page=="Main_Page_en.wikipedia.org_all-access_all-agents")
main.all.all.ts <- main.all.all %>% gather(key=date, value=views, -Page)
main.all.all.ts$date <- sub("X", "", main.all.all.ts$date) 
main.all.all.ts$date <- as.Date(main.all.all.ts$date, format="%Y.%m.%d")
main.all.all.ts$index <- 1:nrow(main.all.all.ts) ## (not needed) index for time series data points

summary(main.all.all.ts)

write_csv(main.all.all.ts, "data-input/main-all.csv")
main.all.all.ts <- read_csv("data-input/main-all.csv") ## includes index although not used
```

```{r PLOT MAIN ALL}
chart.title <- "Daily Views for Main page - all access, all agents"
plot.ts1 <- ggplot(main.all.all.ts, aes(x=date, y=views))+geom_line()+
  scale_y_continuous(labels=comma, expand=c(0,0))+theme_classic()+ggtitle(chart.title)
ggplotly(plot.ts1)
```

## Time Series Modeling (single time series example)

Take the example of Main page, all access, all agent to build time series model based on single time series.

### Approach 1: Linear Smoothing (Loess)

References:

* http://r-statistics.co/Loess-Regression-With-R.html (code toward bottom doesn't work)
* http://ggplot2.tidyverse.org/reference/geom_smooth.html

Info:

* Loess is short for 'local regression' - it is the most common method for smoothing volatile time series
* Uses least squares regression on subsets of data (can control how finely grained the subsets are)
* ggplot2 uses loess as default for geom_smooth when less than 1,000 data points
* Loess using lots of memory and so is not suitable for huge data sets

#### Analyze (visualize) smoothing models

SAME CHART AS ABOVE WITH LOESS SMOOTHING ADDED (ggplot2 defaults)

```{r PLOT MAIN ALL SMOOTH}
chart.title <- "Daily Views with Loess Smoothed Line"
plot.ts1+geom_smooth(method='loess')+ggtitle(chart.title)
```

* Increase granularity with span (between 0-1, higher is smoother)

```{r PLOT MAIN ALL SMOOTH 2}
chart.title <- "Same Plot with loess span set lower for more granularity"
plot.ts1+geom_smooth(method='loess', span=0.3)+ggtitle(chart.title)
```

* can layer in multiple loess smoothed lines for comparison (confidence intervals removed)

```{r ALTERNATIVE SMOOTHED LINES}
chart.title <- "Same Plot with various smoothing lines (span adjusted, no conf. int.)"
plot.ts1+
  geom_smooth(formula=y ~ x, method='loess', span=0.2, color='red', se=FALSE)+
  geom_smooth(method='loess', span=0.4, color='orange', se=FALSE)+
  geom_smooth(method='loess', span=0.6, color='green', se=FALSE)+
  geom_smooth(method='loess', span=0.8, color='purple', se=FALSE)+
  ggtitle(chart.title)

```

#### Making a Prediction based on loess model

Get loess model from existing data

```{r LOESS MODEL}
## Loess model
## can use 'index' or just convert date to numeric
loess1 <- loess(views ~ as.numeric(date), data=main.all.all.ts, span=0.3)
summary(loess1)

```

Apply Loess model to future time periods

```{r PREDICITON WITH LOESS}
## extend date range for prediction period
ndays <- 45 ## number of days to predict
pred.period <- data.frame(date=seq(min(main.all.all.ts$date),max(main.all.all.ts$date+ndays), by='days'))

## prediction with loess1 doesn't work because default loess doesn't extrapolate 
#predict(loess1, pred.period, se=TRUE)

## new loess model: add control=...
sp <- 0.45 ## set span for model: lower number puts more weight on recent
loess2 <- loess(views ~ as.numeric(date), data=main.all.all.ts, control=loess.control(surface = 'direct'), span=sp)

## plot actual data with fitted data from model
chart.title <- "Daily Views with Loess Model fitted"
plot.ts1+geom_line(aes(date, loess2$fitted, color='model'))+ggtitle(chart.title)

## predict with new loess model - extended period
pr <- predict(loess2, as.numeric(pred.period$date), se=TRUE)
## prediction (including existing data)
#pr[[1]] ## first object is prediction

## new data frame with dates and prediction
prediction <- pred.period %>% mutate(views.pred=pr[[1]])

## join date rate for prediction with existing data
main.pred <- left_join(prediction, main.all.all.ts, by='date') %>% select(-index)

## plot the result
chart.title <- "Daily Views for Main Page with Loess Model Prediction"
plot.ts2 <- ggplot(main.pred, aes(x=date, y=views))+geom_line()+
  scale_y_continuous(labels=comma, expand=c(0,0))+theme_classic()+
  ggtitle(chart.title)+geom_line(aes(date, views.pred, color='model+prediction'))
ggplotly(plot.ts2)

```

Span: `r sp`
Number of days predicted: `r ndays`

#### Conclusion

* Loess is great for smoothing a line to highlight general pattern
* maybe not great for time series prediction - subject to manipulation

### Approach 2

Reference:
* http://r-statistics.co/Time-Series-Analysis-With-R.html

#### Convert data from data frame to time series object

* Set up time series so that can apply time series functions for decomposition, etc

```{r TIME SERIES MAIN}
## time series forumlation examples from above reference
# ts (inputData, frequency = 4, start = c(1959, 2)) # frequency 4 => Quarterly Data
# ts (1:10, frequency = 12, start = 1990) # freq 12 => Monthly data. 
# ts (inputData, start=c(2009), end=c(2014), frequency=1) # Yearly Data

## Convert data frame to time series: daily frequency
ts.Main <- ts(main.all.all.ts$views, frequency=365, start=c(year(min(main.all.all.ts$date)), month(min(main.all.all.ts$date)), day(min(main.all.all.ts$date))))

## Alternate: See Notes below for explanation of frequency
ts.Main.all.all.wk <- ts(main.all.all.ts$views, frequency=52, start=c(year(min(main.all.all.ts$date)), month(min(main.all.all.ts$date)), day(min(main.all.all.ts$date))))

```

Notes:

* since it is daily data, time series frequency=365 (days in yr)
* however, because there is total 550 data points, not enough data for seasonality component to be estimated (need at least two iterations)
    + will get error: "time series has no or less than 2 periods""
* so...used frequency=52 to treat the time series as weekly data for illustration purposes
* (great for illustrative purposes but might be hard to get a reliable prediction)

More on 'time series has no or less than 2 periods' error: <br />
* https://stat.ethz.ch/pipermail/r-help/2013-October/361047.html

#### Decomposition

Using 'decompose'

```{r TIME SERIES MAIN DECOMP}
decomposedRes <- decompose(ts.Main.all.all.wk, type='additive') ## type='mult' if multiplicative; 'additive' if additive
plot(decomposedRes)

```

Using 'stl'

```{r TIME SERIES MAIN STL}

stl.style <- stl(ts.Main.all.all.wk, s.window='periodic')
plot(stl.style)

```

#### Prediction

https://a-little-book-of-r-for-time-series.readthedocs.io/en/latest/

Reverting back to original data and forging ahead with prediction.

```{r PREDICTION 2}
## back to daily data even though less than 2 periods
ts.Mainforecast <- HoltWinters(ts.Main, beta=FALSE, gamma=FALSE)
ts.Mainforecast
```

* alpha close to 1 means heavy weighting on recent (needs confirmation)

```{r}
plot(ts.Mainforecast)
```

* plotting forecast against actual

#### Forecast

```{r}
## requires 
library(forecast)
library(stats)
ts.Mainforecast2 <- forecast(ts.Mainforecast, h=45) ## don't need forecast.HoltWinters()
ts.Mainforecast2

plot(ts.Mainforecast2)


```

